Revision as of 00:30, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>If <math>H\in M_M(\mathbb T)</math> and <math>K\in M_N(\mathbb T)</math> are complex Hadamard matrices, prove that so is the matrix <math display="block"> H\otimes_QK\in M_{MN}(\mathbb T) </math> given by the following formula, with <math>Q\in M_{M\times N}(\mathbb T)</math>, <math display="block"> (H\otimes_QK)_{ia,jb}=Q_{ib}H_{ij}K_{ab} </math> called Di\c t\u a deformation of <math>H\otimes K</ma...")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
If [math]H\in M_M(\mathbb T)[/math] and [math]K\in M_N(\mathbb T)[/math] are complex Hadamard matrices, prove that so is the matrix
[[math]]
H\otimes_QK\in M_{MN}(\mathbb T)
[[/math]]
given by the following formula, with [math]Q\in M_{M\times N}(\mathbb T)[/math],
[[math]]
(H\otimes_QK)_{ia,jb}=Q_{ib}H_{ij}K_{ab}
[[/math]]
called Di\c t\u a deformation of [math]H\otimes K[/math], with parameter [math]Q[/math].